RU2562153C1 - Determination of fields of numerical concentration of disperse phase in aerosol flow and device to this end - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: optical system of lenses and diaphragm created a constant-width laser pane in analyzed area. Concentration of disperse phase is defined by intensity of radiation particles dissipated in said plane. In compliance with this process, disperse phase concentration spatial distribution is obtained at notable number of particles or drops in aerosol flow at axially symmetric stream. Transition from relative units of measurement of disperse phase numerical concentration fields to absolute values id executed by system calibration. Calibration consists in comparison of radiation dissipated by disperse phase with measured magnitude of disperse phase numerical concentration with the help of weight process.

EFFECT: higher accuracy definition of concentration and disperse phase mass density in space, evaluation of disperse phase particles distribution.

2 cl, 12 dwg, 2 tbl

Description

The present invention relates to measuring technique, in particular to non-contact quantitative determination of the spatial distribution of particle concentration (mass and volume) in an aerosol stream without introducing disturbances into it. It can be used for optical sensing of physical processes, visualization, qualitative and quantitative determination of physical parameters in optically inhomogeneous media, including wind tunnels and biological tissues.

Currently, there are many instruments and devices for visualization and quantitative measurement of the parameters of liquid and gas during the flow of bodies around a multiphase stream.

1. The most famous companies Lavision (www.lavision.com), Dantec (www.dantecdynamics.com), as well as the domestic company Polis (http://www.itp.nsc.ru) using the most modern achievements in science and technology (foreign research), produce devices that determine the characteristics and structures of multiphase flows. Known methods for measuring the concentration of particles (weight nephelometers, nephelometers based on the absorption of radiation, etc.) and drops in the stream, when quantitative measurements are carried out only at individual points. The three-dimensional structure of the flow is restored by tomographic multiple photographs of the moving light plane of the laser sheet (eg, www.lavision.com), the radiation intensity of which varies throughout this plane. This greatly complicates image processing and can lead to measurement errors. In this case, to build a laser sheet using a cylindrical lens or rotating mirrors. This inevitably leads to a divergence of the plane of the laser sheet and, as a result, to a decrease in the measurement accuracy.

2. The PDPA method is known - Particle Doppler Phase Analyzer, which consists in measuring the speed, size and concentration of the dispersed phase at the intersection of two laser beams by analyzing changes in the interference pattern (see, for example, S. M. Sipperley and WD Bachalo Triple Interval Phase Doppler Interferometry: Improved Dense Sprays Measurements and Enhanced Phase Discrimination (ILASS Americas, 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013). The disadvantage of this method is the spatial limitedness of the measurements - the ability to obtain values of the flow parameters at only one point in space.

3. There is a known weighted method for determining the dust content and water content of a medium, which consists in separating particles from a known volume of aerosol medium with their subsequent weighing. The device consists of (Volkov E.P., Gavrilov E.I., Duzhin F.P. Gas exhaust pipes of thermal power plants and nuclear power plants // M .: Energoatomizdat. - 1987. - 280 p., Volkov E.P. Gas contamination control by emissions Thermal Power Station // M .: Energoatomizdat. 1986. - 255 p.) Intake pipe (when dust is deposited outside the gas consumption), a device for the deposition of particles, a device for measuring the flow rate of sampled gases and means for exhausting gases. This method has several disadvantages, which include the perturbation of the aerosol stream, the inability to continuously automatically control the distribution of particle concentration in the aerosol stream, and the duration of particle sampling and analysis.

4. A known method of constructing a laser sheet using a rotating mirror (see, for example, www.laserpribor.ru). The rotating mirror method inevitably leads to divergence of radiation rays and difficulties in processing the obtained images.

5. Information on the numerical concentration of particles and droplets can also be obtained from analysis of the measurement data by the oil trap method (used, for example, in Miller AB, Potapov Yu.F., Tokarev OD, Yashin A.E. Experimental studies of the formation of barrier ice on conventional and nanomodified surfaces of aviation materials // Materials of the XXIV Scientific and Technical Conference on Aerodynamics in the Village named after V. Volodarsky. - M.: TsAGI Publishing House. - 2013. - P. 179), consisting in introducing into the stream an impactor plate coated with oil into which I get t particles or drops stuck in it. This method is designed to measure the distribution of particles and droplets in the stream by their size, and the error in determining the concentration of particles and droplets can be significant.

6. Information on the numerical concentration of particles in an aerosol stream can also be obtained by analyzing Schlieren images obtained by sensing a dispersed stream (see, for example, William D. Bachalo, Chad Sipperley, and Gregory Payne Aircraft Icing Research: Challenges in Cloud Simulation and Characterization ILASS Americas, ^23nd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA., May 2011). This method allows only a qualitative assessment of the distribution of the numerical concentration of the dispersed phase, because all space filled with particles appears on the path of light, which can lead to significant measurement errors.

The prototype adopted a method for determining the concentration of the dispersed phase in an aerosol stream by the laser sheet method (Vasilevsky E.B., Bezmenov V.Ya., Borovoi V.Ya., Gorelov V.A., Zhilin Yu.V., Kazansky R.A., Mosharov V.E., Chirikhin A.V., Yakovleva L.V. An experimental study of the flow, heat transfer, and electro-optical phenomena during the flow of a supersonic aerodispersed stream around bodies // TsAGI - the main stages of scientific activity 1993-2003 - M .: Fizmatlit , - 2003. - S. 452-457). Using a cylindrical lens, the laser beam is turned into a diverging light plane. In accordance with the discrepancy of this plane find the spatial distribution of the intensity of the probe radiation in space far from the source. The intensity distribution of the radiation scattered by particles in a photograph of a laser sheet determines the distribution of the concentration of the dispersed phase near the streamlined body in relative values. A device for implementing the method comprises a laser radiation source, a cylindrical lens, a photodetector, and digital equipment for processing an image of a laser sheet.

One of the disadvantages of the prototype is the divergence of the rays of the laser sheet and, as a result, the heterogeneity of the intensity of the probe radiation in the plane of the laser sheet, which can significantly reduce the accuracy of obtaining the fields of the numerical concentration of particles and droplets in the aerosol stream. Another disadvantage is that they do not take into account the attenuation of probe radiation in a medium seeded with particles.

The objective and technical result of the invention is to increase the accuracy of determining the spatial distribution of the numerical concentration of particles or droplets in the aerosol stream, as well as the transition from relative measurement values to absolute values.

In addition to the tasks associated with measuring the concentration fields of the dispersed phase, the method can be used for optical sensing of physical processes occurring in hydrodispersed flows, biological tissues, and other optically inhomogeneous media. In addition to the tasks associated with measuring the concentration fields of the dispersed phase, a device for implementing the method can be used to visualize fluid and gas flows, quantitatively measuring (in wind tunnels and biological tissues) flow parameters (speed, density, energy of turbulent pulsations, impurity distribution, and t .P.).

The solution of the problem and the technical result are achieved by the fact that in the method for determining the fields of the numerical concentration of the dispersed phase in the aerosol stream, which consists in creating a laser sheet and analyzing the intensity of the radiation scattered by the particles (dispersed phase) in the light plane of the laser sheet, the concentration fields of the dispersed phase, while creating a laser sheet having a constant width, when processing the data of the optical-physical experiment take into account the attenuation of probe radiation in aerosol cf food; the image of the laser sheet probing the axisymmetric dispersed flux around the bodies is processed along the radiation propagation path, additional information on the flow symmetry is used, the method of successive approximations (iterations) is used to ensure convergence to the correct solution, the optical measurement system is calibrated by comparing the brightness of the scattered radiation on a photograph of a laser sheet and a certain concentration of the dispersed phase by the gravimetric method.

The solution of the problem and the technical result are also achieved by the fact that the device for constructing a laser sheet containing a laser source, a cylindrical lens, a photodetector and digital image processing apparatus for the laser sheet, further comprises a large collecting lens of variable radius of curvature located behind the cylindrical lens, and a diaphragm located behind a large collecting lens to create a laser sheet having a constant width.

FIG. 1. Scheme of optical sensing aerosol flow around a body.

FIG. 2. Scheme for photographing a laser sheet during optical sensing of an aerosol stream around a body (the x axis of the stream is perpendicular to the plane of the figure).

FIG. 3. Optical diagram of a device for constructing a laser sheet of constant width (side view).

FIG. 4. The optical scheme of the device for constructing a laser sheet of constant width (front view).

FIG. 5. The dependence of the maximum angle β of the divergence of the light beam after it passes through the cylindrical lens on the radius r of this lens for various values of the refractive index of the optical glass n _λ .

FIG. 6. The dependence of the distance L on the refractive indices of the optical glasses of the lenses of the system m _λ and n _{λ of} small cylindrical and large collecting lenses, respectively.

FIG. 7. The dependence of the radius of curvature of a large collecting lens on the angle γ for various values of the refractive index of the materials of the lenses of the optical system m _λ = n _λ .

Fig 8. Visualization by the method of a laser sheet of dust and suspension flows.

FIG. 9. The scheme of using information during integration along the radiation propagation path. The x axis of the flow is perpendicular to the plane of the figure.

FIG. 10. Verification of the image processing method of the laser sheet.

FIG. 11. Scheme for quantitative determination of the spatial distribution of the concentration of particles in the aerosol stream.

, a - радиус частицы, λ=0.63 мкм - длина волны зондирующего излучения.FIG. 12. Dispersion indicators calculated according to Mie theory.

, a is the particle radius, λ = 0.63 μm is the wavelength of the probe radiation.

Let us consider the use of a laser sheet for probing an axisymmetric flow around a blunt body with a supersonic aerosol stream (Fig. 1) with a spatial distribution in a unit volume (hereinafter, concentration) of n (x, y, z) of identical spherical particles of known material and radius a : an example of geometric and physical parameters are shown in table. 1 and 2, respectively.

In FIG. 1 — 1 — plane of the laser sheet, 2 — direction of radiation 3 — direction of the aerosol stream, 4 — streamlined body, 5 — region covered by the photodetector, 6 — lens of the photodetector (photosensitive matrix). The plane of the photodetector lens is parallel to the plane of the laser sheet, the plane of the laser sheet passes through the axis of symmetry of the aerosol stream x and belongs to the plane z = 0. Each particle has its own scattering coefficient Q _sca , absorption coefficient Q _a and attenuation coefficient (extinction) Q _ext = Q _sca + Q _{a of} incident radiation of intensity I ₀ with wavelength λ, which are calculated using the well-known Mie theory (or the Rayleigh formula in the case small particles) depending on the electromagnetic properties of the particle material and their size. Neglecting the multiple dissipation of radiation energy, we obtain a formula relating radiation in each cell of a photograph of the light plane (laser sheet) and the concentration of particles n in the probed volume.

в каждой точке A(x, y) плоскости z=0 лазерного листа (фиг. 1) пропорциональна концентрации частиц n(x, y, 0) в малой окрестности этой точки, толщине ножа h, а также коэффициенту рассеивания излучения πa ²Q_sca(a) при заданной длине волны. Здесь индекс i означает incident (падающий).Radiation intensity $$I_A^i\left(x,y\right)$$

at each point A (x, y) of the z = 0 plane of the laser sheet (Fig. 1), it is proportional to the particle concentration n (x, y, 0) in a small neighborhood of this point, the knife thickness h, and also the radiation scattering coefficient π a ² Q _sca ( a ) at a given wavelength. Here the index i means incident (falling).

In this case, one should take into account the attenuation of radiation along the y axis, since, passing to a given point, the light energy decays according to the well-known exponential law (Bouguer) as a result of its scattering and absorption by aerosol particles (molecular scattering and absorption are small: it does not make sense to take them into account )

Each point on the plane of the laser sheet is one-to-one displayed on the photograph. From each luminous (as a result of scattering) cell of the light plane of the sheet, the radiant energy, fading out, passes through the objective lens (Fig. 2) to the corresponding point S (x _M , y _M ) of the photodetector matrix, and the expression for the signal intensity I _e (xx _M (x), y _M (y)) at an arbitrary point S (x _M , y _M ) in the photograph will be as follows:

where s is the path traveled by light from a point on the plane of the laser sheet A (x, y) to point S (x _M (x), y ₀ (y)), on the plane of the photosensitive matrix: a photograph. The small area A ₁ A ₂ and the segment AL form a solid angle Ω, inside which there is a loss of radiant energy (Fig. 2) that has fallen into the photodetector from the sheet plane element A ₁ A ₂ .

, где Z - расстояние от плоскости лазерного листа до фотоприемника. Концентрация частиц при интегрировании вдоль пути s определяется следующим выражением n(s)=n(ξ (s), η(s), ζ(s)). Входящие в него величины находятся из геометрии фиг. 1: ξ(s)=s sinεcosφ, η(s)=ssinεsinφ, ζ(s)=scosε. Из геометрии (Фиг. 1) также находим входящие в них углы: $$tg\epsilon =\sqrt{x^2+y^2}/Z$$

, tgψ=y/x.In FIG. 2 shows 1 — laser sheet, 2 — direction of radiation, 4 — streamlined body, 6 — photosensitive photodetector matrix: image of an object, 7 — photodetector lens. The entire path from point A to point S is determined by the expression $$\text{As}=\sqrt{{\left(\text{x}-{\text{x}}_{\text{M}}\right)}^{\text{2}}+{\left(\text{y}-{\text{y}}_{\text{M}}\right)}^{\text{2}}+{\text{<figure-callout id="2" label="Z" filenames="00000066.png,00000067.png" state="{{state}}">Z</figure-callout>}}^{\text{2}}}$$

where Z is the distance from the plane of the laser sheet to the photodetector. The concentration of particles during integration along the path s is determined by the following expression n (s) = n (ξ (s), η (s), ζ (s)). The values included in it are found from the geometry of FIG. 1: ξ (s) = s sinεcosφ, η (s) = ssinεsinφ, ζ (s) = scosε. From the geometry (Fig. 1) we also find the angles included in them: $$tg\epsilon =\sqrt{x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}/Z$$

, tgψ = y / x.

In FIG. 3 and FIG. 4 shows diagrams (Fig. 3 is a side view and Fig. 4 is a front view) of a device for constructing a laser sheet. A device for constructing a laser sheet 1 of constant width consists of a cylindrical lens (constant radius of curvature r) 8, a large collecting lens with a variable radius of curvature 9, aperture 10, slit 11. The beam of laser radiation 12, passing through the optical system described above, is converted into plane-parallel a beam of rays 13 (having an elliptical shape in its cross section), which, after cutting with a diaphragm, is converted into a thin laser sheet of constant width.

We write the well-known Snell law for the refraction of light rays passing through the lenses (see Fig. 3):

Here n _λ and m _λ are the refractive indices of the materials of which the first and second lenses are made, respectively. The maximum values of the angles α and β are determined by the diameter of the input laser beam d: and the radius of curvature r of the first (cylindrical) lens:

In FIG. Figure 5 shows the dependences of the maximum angle β for various values of the refractive index of the optical glass of a cylindrical lens.

After passing through a cylindrical concave lens 8 (see Fig. 3), the laser beam is converted into a diverging light plane. This diverging plane (fan) is converted into a plane-parallel laser sheet after passing through a large collecting lens 9 of variable radius of curvature.

O ₂ D + FD-O ₁ F = O ₂ D + FD- [O ₁ B + FB] = O ₁ O ₂ = L, where L is the distance between the centers of curvature of the cylindrical and large collecting lenses,

or

Here the angles α and β depend on the angle γ:

The value of L is found based on the diameter of the input beam d and the width of the laser sheet D:

Or

Thus, L depends only on the refractive indices of the lenses n _λ and m _λ .

In FIG. Figure 6 shows the dependence of the lengths L on the refractive indices of the optical glasses of which the lenses are made.

And the radius of curvature is expressed by the following formula:

Here n _λ is the refractive index of the material from which the lenses are made, R (γ) is the radius of curvature of the lens; L is the distance between the centers of curvature of the lenses.

In FIG. Figure 7 shows the dependence of the radius R (γ) of the curvature of a large collecting lens for various values of the refractive index of the material from which the lenses are made: n _λ = 1.1-2.0.

The stream of parallel rays obtained by the passage of light through a large collecting lens 9 has the form of an ellipse 13 in a flat section (Fig. 3, 4). To create a flat laser sheet 1 (Fig. 3), this ellipse must be “cut off” by passing it through the diaphragm 10 (Fig. 3, 4) with a slit 11 (Fig. 3, 4). By varying the width of the slit 11, the optimal thickness of the plane of the laser sheet is selected for effective optical sensing of multiphase flows.

In FIG. Figure 8 shows laser-dust visualization of gas-dust and suspension flows.

We describe the image processing method. Let I _e be the radiation intensity field in the photograph, which was obtained by photographing the plane of the laser sheet probing the aerosol flow around the body (Fig. 1). We divide the photograph — the computational domain into Nx and Ny cells along the x and y axes, respectively. Let i, j be the cell numbers along the x and y coordinate axes, respectively (i ∈ [1, N _x +1], j ∈ [1, N _y +1]), and I _e (i, j) be the radiation intensity in the cell with numbers i, j. It is required to find the spatial distribution of particle concentration near a blunt body using the photograph described above: solve the inverse problem. There are methods for solving such problems (Tikhonov A.N., Arsenin V.Ya. Methods for solving ill-posed problems // M .: Nauka. Gl. Ed. Phys.-Math. Lite. - 1986. - 288 p .; Alifanov O. M. Inverse heat transfer problems // M .: Mechanical Engineering. - 1988. - 280 s .; Beck J., Blackwell B., St. Claire C. Incorrect Inverse Problems // M .: Mir. - 1989. - 312 p. ), based mainly on the use of additional a priori information and a sequential (iterative) approximation to the solution.

The basic principles of the developed image processing method are that

1. computer processing of the image is carried out along the path of propagation of the energy of the probe radiation in the photograph;

2. use information on the symmetry of the distribution of particles relative to the x axis of the two-phase flow during axisymmetric flow around a blunt body;

3. use the method of successive approximations, while the iterative algorithm provides a negligible error in image processing.

In FIG. 9 is a diagram of using information in processing an image of a laser sheet, where the plane of the laser sheet 1, the direction of incident radiation 2, the direction of scanning when processing the image 3, the direction of radiation entering the photodetector 4, lines of equal concentration of the dispersed phase 5, the photodetector lens 6, photosensitive matrix: image of an object 7. We describe a numerical method for solving the inverse problem by substituting (1) in (2) and writing (2) in the following form:

Here β = π a ² Q _ext is the attenuation (extinction) of the radiation, the coefficient α relates the radiation intensity in the image I _e with the concentration of the dispersed phase n in the stream during optical sounding of the aerosol stream.

In the upper region of the laser sheet, the light energy did not weaken as a result of scattering along the y axis (Fig. 9), because

или

Поэтому целесообразно обрабатывать фотоснимок (сканировать) сверху вниз: в направлении зондирующего излучения для получения распределения концентрации дисперсной фазы. Ниже на малую величину Δy (шаг разбиения области по вертикали) концентрация частиц в первом приближении (первой итерации) равнаand the particle concentration is

or

Therefore, it is advisable to process the photograph (scan) from top to bottom: in the direction of the probe radiation to obtain the distribution of the concentration of the dispersed phase. Below by a small value Δy (step of dividing the region vertically), the concentration of particles in a first approximation (first iteration) is

or

нужен для того, чтобы найденное в первом приближении значение концентрации частиц не превосходило искомого значения концентрации частиц, которое требуется найти. Отладка алгоритма показала, что в противном случае решение не будет сходиться с ростом числа приближений. Во втором приближении (итерации) концентрация частиц вычисляется, используя значение концентрации частиц в данной ячейке в первом приближении $$\underset{1}{n(i\mathrm{,2})}$$

. При этом ослабление излучения между первой и второй ячейкой равно произведению β на шаг разбиения расчетной области по вертикали Δy и на среднее значение концентрации частиц между этими ячейками. Концентрация частиц во втором приближении равнаThis value is less than the particle concentration value that needs to be obtained and which will subsequently be found by the method of successive approximations: the iteration method. Factor $$\frac{\text{one}}{\text{2}}$$

needed so that the particle concentration value found in the first approximation does not exceed the desired particle concentration value that needs to be found. Debugging the algorithm showed that otherwise the solution will not converge with an increase in the number of approximations. In the second approximation (iteration), the particle concentration is calculated using the particle concentration in this cell in the first approximation $$\underset{\mathrm{one}}{n(i\mathrm{,\; 2})}$$

. In this case, the attenuation of radiation between the first and second cells is equal to the product β by the step of dividing the computational domain vertically Δy and the average particle concentration between these cells. The particle concentration in the second approximation is equal to

Further, the process can be repeated many times to ensure the required accuracy:

Striving for the number of iterations p → ∞, we obtain the value of the concentration of the dispersed phase n in cell (i, 2) up to a numerical approximation. The experience of predecessors (Tikhonov A.N., Arsenin V.Ya. Methods for solving ill-posed problems // M .: Nauka. Gl. Ed. Phys.-Math. Lit. - 1986. - 288 p .; Alifanov OM heat transfer problems // M .: Mechanical Engineering. - 1988. - 280 p.) indicates the effectiveness of iterative methods for solving inverse problems. Continuing to act in a similar way, they find the value of the concentration of the dispersed phase in the third cell vertically, while noting that the numbering of the cells is counted from the place where the radiation enters the calculation region, i.e. top down:

в первом приближении,

as a first approximation

- во втором и последующих приближениях.

- in the second and subsequent approximations.

Carrying out a scan in the direction of radiation propagation s in a similar way, having caught the pattern, the values of the concentration of the dispersed phase in the remaining j _s = N _y + 1-j cells are found:

в первом приближении,

as a first approximation

- во втором и последующих приближениях.

- in the second and subsequent approximations.

Taking into account the attenuation of the radiation intensity along the path from the plane of the laser sheet to the photodetector, in addition to scanning along the radiation propagation and the method of successive approximations, a priori information on symmetry about the flow axis x of the dispersion phase concentration distribution is used to solve the inverse optical problem of finding the spatial distribution of the dispersed phase by the intensity of the radiation.

In the upper region of the laser sheet, the radiation intensity did not weaken as a result of scattering both along the y axis and along the z axis (see Fig. 9), because optical paths (along y and z) traveled by radiation are zero

или

В следующей ячейке, ниже на малую величину Δy концентрация частиц в первом приближении (первой итерации) равнаThe integral along the z axis is zero, because when the distance from the x axis is greater than the value of H, the dispersed phase is absent (see Fig. 9). Therefore, the concentration of particles in the upper cell of the computational domain is

or

In the next cell, lower by a small Δy value, the concentration of particles in the first approximation (first iteration) is

Where Δ ₁₂ is the first and only (see Fig. 4) cell along the z axis, which corresponds to the second scanning cell

Here

нужен для того, чтобы найденное в первом приближении значение концентрации частиц не превосходило значение концентрации частиц, которое требуется найти. Отладка алгоритма показала, что в противном случае решение не будет сходиться с ростом числа приближений. Во втором приближении (итерации) концентрацию частиц вычисляют, при этом используют значение концентрации частиц в этой ячейке в первом приближении $$\underset{1}{n(i\mathrm{,2})}$$

. При этом ослабление излучения по вертикали равно произведению β на шаг разбиения расчетной области по вертикали Δy и на среднее значение концентрации частиц между этими ячейками, а ослабление на пути z равно произведению β на шаг разбиения расчетной области вдоль z Δ₁₂ и на среднее значение концентрации частиц между этими ячейками. Концентрация частиц во втором приближении равнаThe obtained particle concentration value in this cell is less than the particle concentration value that is required to be obtained and which is subsequently found by the method of successive approximations: iteration method. Factor $$\frac{\mathrm{one}}{2}$$

needed so that the particle concentration value found in the first approximation does not exceed the particle concentration value that you want to find. Debugging the algorithm showed that otherwise the solution will not converge with an increase in the number of approximations. In the second approximation (iteration), the concentration of particles is calculated, while using the value of the concentration of particles in this cell in the first approximation $$\underset{\mathrm{one}}{n(i\mathrm{,\; 2})}$$

. In this case, the vertical attenuation of radiation is equal to the product β by the vertical step of dividing the computational domain Δy and the average particle concentration between these cells, and the attenuation along the path z is the product of β by the step of dividing the computational domain along z Δ ₁₂ and the average particle concentration between these cells. The particle concentration in the second approximation is equal to

Further, the process can be repeated many times to ensure the required accuracy:

By striving for the number of iterations p → ∞, we obtain the value of the concentration of the dispersed phase n in cell (i, 2) up to a numerical approximation. Continuing to act in a similar way, they find the value of the concentration of the dispersed phase in the third cell vertically:

- в первом приближении,

- as a first approximation,

- во втором и последующих приближениях.

- in the second and subsequent approximations.

- величина ячейки ВС (фиг. 9), $${\text{y}}_{\text{j}{}_{\text{s}}}=\text{H}-\left({\text{j}}_{\text{s}}-\text{1}\right)\text{Δy}$$

,

Here $${\text{Δ}}_{{\text{j}}_{\text{s}}\text{, k}}=\left({\text{tanα}}_{{\text{j}}_{\text{s}}}^{\text{k}-\text{one}}-{\text{tanα}}_{{\text{j}}_{\text{s}}}^{\text{k}}\right){\text{y}}_{{\text{j}}_{\text{s}}}$$

- the value of the cell BC (Fig. 9), $${\text{y}}_{\text{j}{}_{\text{s}}}=\text{H}-\left({\text{j}}_{\text{s}}-\text{one}\right)\text{Δy}$$

,

. Проводят сканирование по направлению распространения излучения s и используют информацию о симметрии относительно оси x, аналогичным образом, уловив закономерность, находят значения концентрации дисперсной фазы в остальных j_s=N_y+1-j ячейках:Thus, the value of an arbitrary cell BC is $$(H-(j-\mathrm{one})\Delta y){\Delta }_{j_s,k}$$

. A scan is carried out in the direction of propagation of radiation s and information on symmetry about the x axis is used, likewise, having caught the pattern, the concentration of the dispersed phase in the remaining j _s = N _y + 1-j cells is found:

as a first approximation

in the second and subsequent approximations.

где

характерная длина пробега излучения

- толщина сжатого слоя вблизи обтекаемой сферы) метод может дать значительную ошибку, т.к. известный экспоненциальный закон ослабления Бугера-Ламберта-Бера не выполняется.The debugging of the algorithm showed that the iterative process converges (the maximum error is less than 0.0001%) in no more than 10 iterations in the parameter range corresponding to the fulfillment of Bouguer's law. Otherwise, the iterative process can lead to an infinitely large error. With significant attenuation of radiation

Where

characteristic mean free path

- the thickness of the compressed layer near the streamlined sphere) the method can give a significant error, because the well-known exponential attenuation law of the Bouguer-Lambert-Beer does not hold.

Thus, the inverse optical problem of reconstructing the distribution of the concentration of particles in the aerodispersed stream by the intensity of the probe radiation scattered by the particles has been solved.

Let us illustrate the operation of the algorithm in a numerical experiment.

(нормированных на концентрацию частиц n₀ у точки торможения), 2 - зарегистрированный фотоприемником оптический сигнал I_e(х_М, y_M), 3 - распределение концентрации частиц, полученное в результате обработки «изображения» 2, 4 - ослабление зондирующего излучения в плоскости лазерного листа, 5 - ослабленное зондирующее излучение на пути от листа до фотоприемника. В результате численного эксперимента, в котором по полю интенсивности излучения на «фотоснимке» (полученному в результате решения прямой задачи (фиг. 10, кривая 2): расчет интенсивности излучения 1е на фотоснимке по заданному распределению концентрации частиц n (фиг. 10, кривая 1), которое качественно описывает поведение дисперсной примеси в экспериментах. (Василевский Э.Б., Безменов В.Я., Боровой В.Я., Горелов В.А., Жилин Ю.В., Казанский Р.А., Мошаров В.Е., Чирихин А.В., Яковлева Л.В. Экспериментальное исследование течения, теплообмена и электрооптических явлений при обтекании тел сверхзвуковым аэродисперсным потоком. // «ЦАГИ - основные этапы научной деятельности 1993-2003» - М.: Физматлит, - 2003. - С. 452-457), в котором методом лазерного листа определялось поле концентрации частиц (фиг. 10, кривая 3) с помощью описанного выше метода и сравнивалось с заданным распределением (фиг. 10, кривая 1). Проведенный расчет (фиг. 10) и отладка описанного выше алгоритма свидетельствуют о ничтожности относительной погрешности определения распределения концентрации дисперсной фазы в аэродисперсном потоке по интенсивности рассеянного ими зондирующего излучения; тем не менее, результат существенно зависит от мелкости разбиения расчетной области: числа ячеек. При сканировании в направлении распространения излучения s необходимым условием сходимости решения обратной задачи является подбор шага разбиения расчетной области таким образом, что

при монотонном возрастании пройденного светом пути s(i, j+1)>s(i, j) в плоскости лазерного листа.In FIG. 10 shows the verification of the image processing method: 1 - distribution of particle concentration $$(n(x=1.25R,\sqrt{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000066.png,00000067.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+z^2}))$$

(normalized to the particle concentration n ₀ at the stagnation point), 2 — optical signal recorded by the photodetector I _e (x _M , y _M ), 3 — distribution of particle concentration obtained as a result of processing the “image” 2, 4 — attenuation of probe radiation in the plane laser sheet, 5 - attenuated probing radiation on the way from the sheet to the photodetector. As a result of a numerical experiment in which, according to the field of radiation intensity in the “photograph” (obtained as a result of solving the direct problem (Fig. 10, curve 2): calculation of the radiation intensity 1e in the photograph from the given distribution of particle concentration n (Fig. 10, curve 1 ), which qualitatively describes the behavior of dispersed impurities in experiments. (Vasilevsky E.B., Bezmenov V.Ya., Borovoy V.Ya., Gorelov V.A., Zhilin Yu.V., Kazansky R.A., Mosharov V .E., Chirikhin A.V., Yakovleva L.V. Experimental study of the flow, heat transfer, and electro-optical phenomena during the flow around bodies with a supersonic aerodispersed stream. // “TsAGI - the main stages of scientific activity 1993-2003” - M .: Fizmatlit, 2003. - P. 452-457), in which the particle concentration field was determined by the laser sheet method (Fig. 10, curve 3) using the method described above and was compared with a given distribution (Fig. 10, curve 1). The calculation (Fig. 10) and debugging of the above algorithm indicate that the relative error in determining the distribution of the concentration of the dispersed phase in the aerodispersed stream is insignificant by intensive the scattered sound of the probe radiation; Nevertheless, the result substantially depends on the fineness of the partition of the computational domain: the number of cells. When scanning in the direction of radiation propagation s, a necessary condition for the convergence of the solution of the inverse problem is the selection of the step for dividing the computational domain in such a way that

with a monotonic increase in the path traveled by light s (i, j + 1)> s (i, j) in the plane of the laser sheet.

Calibration of the measuring system is carried out by comparing the brightness of the scattered radiation in a photograph of a laser sheet and the measured concentration of the dispersed phase by a weight nephelometer. In FIG. 11 is a diagram for quantitatively determining the spatial distribution of particle concentration in an aerosol stream. 2 - the direction of propagation of the probe radiation, 3 - the direction of the aerosol stream, 4 - the streamlined body, 17 - the nozzle, 18 - control volumes in which the particle size distribution in the aerosol stream is measured, 19 - builder of a laser sheet of constant thickness, 20 - flow area designed for calibration of the measuring complex, 21 - weight nephelometer with flow rate sensor. A weight nephelometer 21 with a flow rate sensor is installed in the upper part of the optically probed region 20 (where the radiant energy is least weakened as a result of its absorption and dispersion by particles). Particles are caught in a nephelometer and weighed. Knowing the area of the inlet section of the nephelometer, the flow rate and the mass of particles falling into it per unit time, measure the concentration of particles in absolute units. This concentration corresponds to the brightness of region 20 in a photograph of a laser sheet probing aerosol flow around a body. The attenuation coefficient depends only on the particle material, its radius a and the radiation wavelength λ: β = π a ² Q _ext ( a , λ).

We find the particle size distribution using a halo nephelometer (Lagunov A.S., Bayvel L.P., Gusev B.A. Determination of the dispersed composition of aerosols by light scattering at small angles // Journal of Applied Spectroscopy. - Volume XI. - Issue. 1. - 1969. - S. 98-103 .; Rudakov V.P., Stasenko A.L., Flaksman Y.Sh. Determination of the mass spectrum of particles in a gas-dispersed stream by the method of small-angle scattering // Scientific notes of TsAGI .-- T. XXIV . - No. 2. - 1993. - pp. 114-122. Gorchakov GI, Tokarev OD Evaluation of the aerosol microstructure according to measurements of aureole indicatrixes of scattering light // Sat. Atmospheric radiation and photometry. - Tomsk. - 1988. - P. 22-25; Lyubovtseva Yu.S. Statistical characteristics of a light halo in fog // Izv. AN SSSR. - Atmospheric and Ocean Physics. - 1971 , T. 7. - No. 4. - P. 465-467; Golikov V.I. Instrument for measuring the microstructure of clouds and fogs by the method of small angles // Proceedings of the Main Geophysical Observatory named after A.I. Voeikov.L .: 1964. - Issue 152. - P. 142-159), based on the well-known method of small-angle scattering (according to the scattering indicatrix), the distribution of particles and droplets by their size is determined. Or using the well-known PDPA method (particle Doppler Phase Analyzer) based on the known physical effects of interference and Doppler ((see, e.g., S.M. Sipperley and WD Bachalo Triple Interval Phase Doppler Interferometry: Improved Dense Sprays Measurements and Enhanced Phase Discrimination ILASS Americas, 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013).

The scattering, attenuation and absorption coefficients, respectively, are found from the well-known Gustav Mi formulas (Mie G. Beiträge zur Optik Medien speziell kolloidaler Metallösungen. - Ann. Phys. 25. - P. 377-445. - 1908) depending on the physical properties of the material aerosol particles and the diffraction parameter x = 2π a / λ, depending on the particle radius a and the wavelength λ of the probe radiation.

.Here $$i=\sqrt{-\mathrm{one}}$$

.

The dependence of the indicatrices of the radiation scattered by the particles on their size at a given value of the wavelength is shown in FIG. 12. Having calculated the light-scattering characteristics of individual particles using the above Mie formulas for the scattering coefficients in equation (3), only one unknown remains - the normalization coefficient α:

It is found by calibrating the optical measurement system described above. Thus, it is possible to quantify the concentration of particles and droplets in the aerosol stream in space and time.

Thus, the use of the invention provides an increase in the accuracy of determining the spatial distribution of the numerical concentration of particles or droplets in the aerosol stream, as well as a transition from relative measurement values to absolute values.

Lenses can be manufactured in optical glass factories. A large lens with a variable radius of curvature can be made from a parabolic collecting lens or a collecting lens with a constant radius of curvature by grinding on a lathe. The lenses and aperture on the respective holders can be mounted on an optical bench. After converting the laser beam into a plane-parallel light plane, the latter is directed to the studied area. Using a digital apparatus, an image of the radiation scattered in the plane of the laser sheet is recorded. Image processing of a digital photograph of a laser sheet using the algorithm described above can be implemented using a computer.

The basic principles of the method described above for measuring the fields of the numerical concentration of the dispersed phase in the aerosol stream and a device for its implementation can be developed and used to study the behavior, visualization and determination of other (in addition to the numerical concentration) parameters of multiphase, heterogeneous flows and media.

Claims (2)

1. The method of determining the fields of the numerical concentration of the dispersed phase in the aerosol stream, which consists in creating a laser sheet, by analyzing the intensity of the radiation scattered by the particles in the light plane of the laser sheet, determining the concentration field of the dispersed phase, characterized in that they create a laser sheet having a constant width , when processing data from an optical-physical experiment, the attenuation of probe radiation in an aerosol medium is taken into account; they process an image of a laser sheet probing an axisymmetric dispersed stream around bodies along the radiation propagation path, using additional information about the symmetry of the stream, using the method of successive approximations (iterations) to ensure convergence to the correct solution, calibrating the optical measuring system by comparing the brightness of the scattered light radiation on a photograph of a laser sheet and a certain numerical concentration of the dispersed phase by the gravimetric method. 2. Device for constructing a laser sheet containing a laser source, a cylindrical lens, a photodetector and digital image processing equipment for a laser sheet, characterized in that it further comprises a large collecting lens of variable radius of curvature located behind the cylindrical lens, and a diaphragm located behind the large collecting a lens to create a laser sheet having a constant width.

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